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)=8x^(3)+5],[h(x)=root(3)(x-5)]:} Write (h@f)(x) as an expression in terms of x. (h@f)(x)=

f(x)=8x3+5h(x)=x−53 \begin{array}{l} f(x)=8 x^{3}+5 \\ h(x)=\sqrt[3]{x-5} \end{array} \newlineWrite (h∘f)(x) (h \circ f)(x) as an expression in terms of x x .\newline(h∘f)(x)= (h \circ f)(x)=

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Domain and range of absolute value functions: equationsright chevron icon

Full solution

Q. f(x)=8x3+5h(x)=x−53 \begin{array}{l} f(x)=8 x^{3}+5 \\ h(x)=\sqrt[3]{x-5} \end{array} \newlineWrite (h∘f)(x) (h \circ f)(x) as an expression in terms of x x .\newline(h∘f)(x)= (h \circ f)(x)=
  1. Understand h@f(x)h@f(x): First, we need to understand that (h@f)(x)(h@f)(x) means h(f(x))h(f(x)). This means we will substitute the function f(x)f(x) into the function h(x)h(x) wherever there is an xx.
  2. Substitute f(x)f(x) in h(x)h(x): The function f(x)f(x) is given as f(x)=8x3+5f(x) = 8x^3 + 5. We will substitute this expression for xx in the function h(x)h(x).
  3. Replace xx with f(x)f(x): The function h(x)h(x) is given as h(x)=x−53h(x) = \sqrt[3]{x - 5}. Now we will replace xx with f(x)f(x) to get h(f(x))h(f(x)).\newlineh(f(x))=f(x)−53h(f(x)) = \sqrt[3]{f(x) - 5}
  4. Substitute f(x)f(x) in h(f(x))h(f(x)): Substitute f(x)=8x3+5f(x) = 8x^3 + 5 into the expression for h(f(x))h(f(x)):\newlineh(f(x))=(8x3+5)−53h(f(x)) = \sqrt[3]{(8x^3 + 5) - 5}
  5. Simplify expression inside cube root: Simplify the expression inside the cube root:\newlineh(f(x))=8x3+5−53h(f(x)) = \sqrt[3]{8x^3 + 5 - 5}\newlineh(f(x))=8x33h(f(x)) = \sqrt[3]{8x^3}
  6. Take cube root of 8x38x^3: Now, we take the cube root of 8x38x^3:
    h(f(x))=8x33h(f(x)) = \sqrt[3]{8x^3}
    h(f(x))=2xh(f(x)) = 2x

More problems from Domain and range of absolute value functions: equations

Question
Find g(x) g(x) , where g(x) g(x) is the translation 2 2 units left of f(x)=∣x∣ f(x) = |x| .\newlineWrite your answer in the form a∣x−h∣+k a|x - h| + k , where a a , h h , and k k are integers.\newlineg(x)= g(x) = ______\newline
Get tutor helpright-arrow

Posted 7 months ago

Question
Find g(x) g(x) , where g(x) g(x) is the reflection across the y y -axis of f(x)=∣x∣ f(x) = |x| .\newlineWrite your answer in the form a∣x−h∣+k a|x - h| + k , where a a , h h , and k k are integers.\newlineg(x)= g(x) = ______\newline
Get tutor helpright-arrow

Posted 11 months ago

Question
The graph of y=∣x∣ y=|x| is reflected across the x x -axis and then scaled vertically by a factor of 77 .\newlineWhat is the equation of the new graph?\newlineChoose 11 answer:\newline(A) y=7∣x∣ y=7|x| \newline(B) y=−7∣x∣ y=-7|x| \newlineC) y=17∣x∣ y=\frac{1}{7}|x| \newline(D) y=−17∣x∣ y=-\frac{1}{7}|x|
Get tutor helpright-arrow

Posted 11 months ago

Question
The graph of y=∣x∣ y=|x| is scaled vertically by a factor of 66 .\newlineWhat is the equation of the new graph?\newlineChoose 11 answer:\newline(A) y=∣x−6∣ y=|x-6| \newline(B) y=6∣x∣ y=6|x| \newline(C) y=16∣x∣ y=\frac{1}{6}|x| \newline(D) y=∣x−16∣ y=\left|x-\frac{1}{6}\right|
Get tutor helpright-arrow

Posted 10 months ago

Question
The graph of y=∣x∣ y=|x| is scaled vertically by a factor of 13 \frac{1}{3} .\newlineWhat is the equation of the new graph?\newlineChoose 11 answer:\newline(A) y=∣x∣−3 y=|x|-3 \newline(B) y=−3∣x∣ y=-3|x| \newline(C) y=13∣x∣ y=\frac{1}{3}|x| \newline(D) y=∣x∣−13 y=|x|-\frac{1}{3}
Get tutor helpright-arrow

Posted 11 months ago

Question
The graph of y=∣x∣ y=|x| is shifted to the left by 66 units.\newlineWhat is the equation of the new graph?\newlineChoose 11 answer:\newline(A) y=∣x+6∣−6 y=|x+6|-6 \newline(B) y=∣x−6∣−6 y=|x-6|-6 \newline(C) y=∣x∣−6 y=|x|-6 \newline(D) y=∣x+6∣ y=|x+6|
Get tutor helpright-arrow

Posted 10 months ago

Question
The graph of y=∣x∣ y=|x| is reflected across the x x -axis and then scaled vertically by a factor of 14 \frac{1}{4} .\newlineWhat is the equation of the new graph?\newlineChoose 11 answer:\newline(A) y=−4∣x∣ y=-4|x| \newline(B) y=∣x∣−4 y=|x|-4 \newline(C) y=−14∣x∣ y=-\frac{1}{4}|x| \newline(D) y=∣x−4∣ y=|x-4|
Get tutor helpright-arrow

Posted 10 months ago

Question
The graph of y=∣x∣ y=|x| is shifted down by 99 units.\newlineWhat is the equation of the new graph?\newlineChoose 11 answer:\newline(A) y=∣x∣−9 y=|x|-9 \newline(B) y=∣x+9∣ y=|x+9| \newline(C) y=∣x∣+9 y=|x|+9 \newline(D) y=∣x−9∣ y=|x-9|
Get tutor helpright-arrow

Posted 1 year ago

Question
y=13x+5y=2x \begin{array}{l} y=\frac{1}{3} x+5 \\ y=2 x \end{array} \newlineConsider the given system of equations. If (x,y) (x, y) is the solution to the system, then what is the value of y+x y+x ?
Get tutor helpright-arrow

Posted 5 months ago

Question
13x+3y=4 \frac{1}{3} x+3 y=4 \newline2x−4=2y 2 x-4=2 y \newlineConsider the given system of equations. If (x,y) (x, y) is the solution to the system, then what is the value of x−y x-y ?
Get tutor helpright-arrow

Posted 4 months ago

View all (19)

Related topics

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