Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

{:[f(x)=6-(1)/(2)x],[h(x)=4(x-3)^(2)]:} Write f(h(x)) as an expression in terms of x. f(h(x))=

f(x)=6−12xh(x)=4(x−3)2 \begin{array}{l} f(x)=6-\frac{1}{2} x \\ h(x)=4(x-3)^{2} \end{array} \newlineWrite f(h(x)) f(h(x)) as an expression in terms of x x .\newlinef(h(x))= f(h(x))=

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Compare linear and exponential growthright chevron icon

Full solution

Q. f(x)=6−12xh(x)=4(x−3)2 \begin{array}{l} f(x)=6-\frac{1}{2} x \\ h(x)=4(x-3)^{2} \end{array} \newlineWrite f(h(x)) f(h(x)) as an expression in terms of x x .\newlinef(h(x))= f(h(x))=
  1. Identify functions and composition: Identify the given functions and the composition we need to find.\newlineWe have two functions:\newlinef(x)=6−12xf(x) = 6 - \frac{1}{2}x\newlineh(x)=4(x−3)2h(x) = 4(x - 3)^2\newlineWe need to find the composition f(h(x))f(h(x)), which means we will substitute h(x)h(x) into f(x)f(x) where xx is.
  2. Substitute h(x)h(x) into f(x)f(x): Substitute h(x)h(x) into f(x)f(x).\newlineTo find f(h(x))f(h(x)), we replace every xx in f(x)f(x) with h(x)h(x):\newlinef(h(x))=6−(12)h(x)f(h(x)) = 6 - \left(\frac{1}{2}\right)h(x)\newlineNow we need to substitute the expression for h(x)h(x) into this new function.
  3. Perform the substitution: Perform the substitution.\newlineSubstitute h(x)=4(x−3)2h(x) = 4(x - 3)^2 into the expression for f(h(x))f(h(x)):\newlinef(h(x))=6−12(4(x−3)2)f(h(x)) = 6 - \frac{1}{2}(4(x - 3)^2)
  4. Simplify the expression: Simplify the expression.\newlineNow we simplify the expression by distributing the 12\frac{1}{2} into 4(x−3)24(x - 3)^2:\newlinef(h(x))=6−2(x−3)2f(h(x)) = 6 - 2(x - 3)^2
  5. Expand the squared term: Expand the squared term (if necessary).\newlineIn this case, we can leave the expression in its factored form, as it is already simplified. So, the final expression for f(h(x))f(h(x)) is:\newlinef(h(x))=6−2(x−3)2f(h(x)) = 6 - 2(x - 3)^2

More problems from Compare linear and exponential growth

Question
Jill bought a used motorcycle from a seller online for $1,200. The seller will charge her $5 a day to store the motorcycle at his house until she is able to pick it up. You can use a function to describe the total amount of money Jill will owe the seller if she waits xx days to pick up the motorcycle.\newlineWrite an equation for the function. If it is linear, write it in the form g(x)=mx+bg(x) = mx + b. If it is exponential, write it in the form g(x)=a(b)xg(x) = a(b)^x.\newlineg(x)=‾g(x) = \underline{\hspace{3em}}
Get tutor helpright-arrow

Posted 7 months ago

Question
How does f(t)=−2t−7f(t)=-2t-7 change over the interval from t=−7t=-7 to t=−6t=-6?\newlineChoices:\newline[f(t) decreases by 2]\left[\text{f(t) decreases by } 2\right]\newline[f(t) increases by 2]\left[\text{f(t) increases by } 2\right]\newline[f(t) increases by 200%]\left[\text{f(t) increases by } 200\%\right]\newline[f(t) decreases by a factor of 2]\left[\text{f(t) decreases by a factor of } 2\right]
Get tutor helpright-arrow

Posted 8 months ago

Question
How does g(t)=9tg(t)=9^t change over the interval from t=1t=1 to t=3t=3?\newlineChoices: \newline[g(t) decreases by a factor of 81]\left[\text{g(t) decreases by a factor of } 81\right]\newline[g(t) increases by a factor of 81]\left[\text{g(t) increases by a factor of } 81\right]\newline[g(t) increases by 18%]\left[\text{g(t) increases by } 18\%\right]\newline[g(t) decreases by 9%]\left[\text{g(t) decreases by } 9\%\right]
Get tutor helpright-arrow

Posted 7 months ago

Question
Both of these functions grow as xx gets larger and larger. Which function eventually exceeds the other?\newline Choices:\newline(A)f(x)=8x+3.3(A)f(x) = 8x + 3.3\newline(B)g(x)=3.3x−5(B)g(x) = 3.3^x - 5
Get tutor helpright-arrow

Posted 8 months ago

Question
Both of these functions grow as x x gets larger and larger. Which function eventually exceeds the other?\newlineChoices:\newline(A) f(x)=2x+9(A) \ f(x) = 2x + 9 \newline(B) g(x)=2x(B)\ g(x) = 2^x
Get tutor helpright-arrow

Posted 8 months ago

Question
The functions f(x) f(x) and g(x) g(x) are differentiable. \newlineThe function h(x) h(x) is defined as: h(x)=g(x)f(x) h(x)=\frac{g(x)}{f(x)} \newlineIf f(8)=1 f(8)=1 , f′(8)=−6 f'(8)=-6 , g(8)=8 g(8)=8 , and g′(8)=−10 g'(8)=-10 , what is h′(8) h'(8) ? \newlineSimplify any fractions. \newlineh′(8)= h'(8)= ______
Get tutor helpright-arrow

Posted 8 months ago

Question
The functions p(x) p(x) and q(x) q(x) are differentiable. \newlineThe function r(x) r(x) is defined as: r(x)=p(x)q(x) r(x)= \frac{p(x)}{q(x)} \newlineIf p(3)=2 p(3)= 2 , p′(3)=4 p'(3)= 4 , q(3)=6 q(3)= 6 , and q′(3)=9 q'(3)= 9 , what is r′(3) r'(3) ? \newlineSimplify any fractions. \newliner′(3)= r'(3)= _____
Get tutor helpright-arrow

Posted 9 months ago

Question
The functions u(x) u(x) and v(x) v(x) are differentiable. \newlineThe function w(x) w(x) is defined as: w(x)=u(x)v(x) w(x)= \frac{u(x)}{v(x)} \newlineIf u(5)=3 u(5)= 3 , u′(5)=−2 u'(5)= -2 , v(5)=7 v(5)= 7 , and v′(5)=1 v'(5)= 1 , what is w′(5) w'(5) ? \newlineSimplify any fractions. \newlinew′(5)= w'(5)= _____
Get tutor helpright-arrow

Posted 9 months ago

Question
The functions a(x) a(x) and b(x) b(x) are differentiable. \newlineThe function c(x) c(x) is defined as: c(x)=a(x)b(x) c(x)= \frac{a(x)}{b(x)} \newlineIf a(2)=4 a(2)= 4 , a′(2)=5 a'(2)= 5 , b(2)=1 b(2)= 1 , and b′(2)=−3 b'(2)= -3 , what is c′(2) c'(2) ? \newlineSimplify any fractions. \newlinec′(2)= c'(2)= _____
Get tutor helpright-arrow

Posted 9 months ago

Question
The functions m(x) m(x) and n(x) n(x) are differentiable. \newlineThe function o(x) o(x) is defined as: o(x)=m(x)n(x) o(x)= \frac{m(x)}{n(x)} \newlineIf m(7)=2 m(7)= 2 , m′(7)=−1 m'(7)= -1 , n(7)=4 n(7)= 4 , and n′(7)=8 n'(7)= 8 , what is o′(7) o'(7) ? \newlineSimplify any fractions. \newlineo′(7)= o'(7)= _____
Get tutor helpright-arrow

Posted 9 months ago

View all (345)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant