Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

f(x)=2x^(3)+8

h(x)=root(3)(12-5x)
Write
(f@h)(x) as an expression in terms of
x.

(f@h)(x)=

$f(x)=2 x^{3}+8$ $\newline$ $h(x)=\sqrt[3]{12-5 x}$ $\newline$ Write $(f \circ h)(x)$ as an expression in terms of $x$ . $\newline$ $(f \circ h)(x)=$

View step-by-step help

View step-by-step help

Compare linear and exponential growth

Full solution

Q.

f(x)=2 x^{3}+8

\newline

h(x)=\sqrt[3]{12-5 x}

\newline

Write

(f \circ h)(x)

as an expression in terms of

x

.

\newline

(f \circ h)(x)=

Substitute $h(x)$ into $f(x)$ : To find the composition of the functions $(f \circ h)(x)$ , we need to substitute the function $h(x)$ into the function $f(x)$ . This means we will replace every instance of $x$ in $f(x)$ with $h(x)$ .
Write down $h(x)$ : First, let's write down the function $h(x)$ : $h(x) = \sqrt[3]{12-5x}$ . This is the cube root of $(12-5x)$ .
Write down $f(x)$ : Now, let's write down the function $f(x)$ : $f(x) = 2x^{3} + 8$ .
Cube root of $(12-5x)$ : Substitute $h(x)$ into $f(x)$ to get $(f@h)(x)$ : $(f@h)(x) = f(h(x)) = 2(h(x))^{3} + 8$ .
Replace cubed $h(x)$ : Now we need to cube the expression for $h(x)$ : $\left(\sqrt[3]{12-5x}\right)^{3}$ . When we cube a cube root, they cancel each other out, so we are left with the expression inside the cube root, which is $12-5x$ .
Simplify the expression: Replace the cubed $h(x)$ in the expression for $(f@h)(x)$ : $(f@h)(x) = 2(12-5x) + 8$ .
Multiply through the expression: Now we simplify the expression: $(f@h)(x) = 2 \times 12 - 2 \times 5x + 8$ .
Combine like terms: Multiply through the expression: $(f@h)(x) = 24 - 10x + 8$ .
Final expression: Combine like terms to get the final expression for $(f@h)(x)$ : $(f@h)(x) = 32 - 10x$ .

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

x

days to pick up the motorcycle.

\newline

Write an equation for the function. If it is linear, write it in the form

g(x) = mx + b

. If it is exponential, write it in the form

g(x) = a(b)^x

\newline

g(x) = \underline{\hspace{3em}}

Posted 5 months ago

Question

f(t)=-2t-7

change over the interval from

t=-7

t=-6

\newline

\newline

\left[\text{f(t) decreases by } 2\right]

\newline

\left[\text{f(t) increases by } 2\right]

\newline

\left[\text{f(t) increases by } 200\%\right]

\newline

\left[\text{f(t) decreases by a factor of } 2\right]

Posted 5 months ago

Question

g(t)=9^t

change over the interval from

t=1

t=3

\newline

\newline

\left[\text{g(t) decreases by a factor of } 81\right]

\newline

\left[\text{g(t) increases by a factor of } 81\right]

\newline

\left[\text{g(t) increases by } 18\%\right]

\newline

\left[\text{g(t) decreases by } 9\%\right]

Posted 5 months ago

Question

Both of these functions grow as

x

gets larger and larger. Which function eventually exceeds the other?

\newline

\newline

(A)f(x) = 8x + 3.3

\newline

(B)g(x) = 3.3^x - 5

Posted 6 months ago

Question

Both of these functions grow as

x

gets larger and larger. Which function eventually exceeds the other?

\newline

\newline

(A) \ f(x) = 2x + 9

\newline

(B)\ g(x) = 2^x

Posted 6 months ago

Question

f(x)

g(x)

are differentiable.

\newline

h(x)

h(x)=\frac{g(x)}{f(x)}

\newline

f(8)=1

f'(8)=-6

g(8)=8

g'(8)=-10

h'(8)

\newline

Simplify any fractions.

\newline

h'(8)=

Posted 6 months ago

Question

p(x)

q(x)

are differentiable.

\newline

r(x)

r(x)= \frac{p(x)}{q(x)}

\newline

p(3)= 2

p'(3)= 4

q(3)= 6

q'(3)= 9

r'(3)

\newline

Simplify any fractions.

\newline

r'(3)=

Posted 7 months ago

Question

u(x)

v(x)

are differentiable.

\newline

w(x)

w(x)= \frac{u(x)}{v(x)}

\newline

u(5)= 3

u'(5)= -2

v(5)= 7

v'(5)= 1

w'(5)

\newline

Simplify any fractions.

\newline

w'(5)=

Posted 7 months ago

Question

a(x)

b(x)

are differentiable.

\newline

c(x)

c(x)= \frac{a(x)}{b(x)}

\newline

a(2)= 4

a'(2)= 5

b(2)= 1

b'(2)= -3

c'(2)

\newline

Simplify any fractions.

\newline

c'(2)=

Posted 7 months ago

Question

m(x)

n(x)

are differentiable.

\newline

o(x)

o(x)= \frac{m(x)}{n(x)}

\newline

m(7)= 2

m'(7)= -1

n(7)= 4

n'(7)= 8

o'(7)

\newline

Simplify any fractions.

\newline

o'(7)=

Posted 7 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant