0. Functions

Composite functions

Let ƒ(x) = x³, g (x) = sin x and h(x) = √x .

Evaluate h(g( π/2)).

Composite functions

Let ƒ(x) = x³, g (x) = sin x and h(x) = √x.

Find the domain of ƒ o g.

If ƒ(x) = √x and g(x) = x³-2 and , simplify the expressions (ƒ o g) (3), (ƒ o ƒ) (64), (g o ƒ) (x) and (ƒ o g) (x)

Composition of Functions

A balloon’s volume V is given by V = s² + 2s + 3 cm³, where s is the ambient temperature in °C. The ambient temperature s at time t minutes is given by s = 2t − 3 °C. Write the balloon’s volume V as a function of time t.

Given the functions $h\left(x\right)=2x^3-4$ and $k\left(x\right)=x^2+2$, find and fully simplify $h\cdot k\left(x\right)$

Given the functions $L\left(x\right)=x-2$ and $M\left(x\right)=x^2$, calculate $\frac{L}{M}\left(5\right)$

Given the functions $f(x)=x+3$ and $g(x)= x^2$ find $(f∘g)(2)$ and $(g∘f)(2)$.

Find functions ƒand g such that ƒ(g(x)) = (x² +1)⁵ . Find a different pair of functions ƒ and g that also satisfy ƒ(g(x)) = (x² +1)⁵  

Use the graphs of ƒ and g in the figure to determine the following function values. y = f(x) ; y=g(x) <IMAGE>

a. (ƒ o g ) (2)

Use the graphs of ƒ and g in the figure to determine the following function values. y = f(x) ; y=g(x) <IMAGE>

b. g (ƒ (2))

Use the graphs of ƒ and g in the figure to determine the following function values. y = f(x) ; y=g(x) <IMAGE>

c. ƒ(g (4))

Use the graphs of ƒ and g in the figure to determine the following function values. y = f(x) ; y=g(x) <IMAGE>

d. g(ƒ(5))

Use the graphs of ƒ and g in the figure to determine the following function values. y = f(x) ; y=g(x) <IMAGE>

e. ƒ(ƒ(8))

Use the table to evaluate the given compositions. <IMAGE>

g(ƒ(4))

Use the table to evaluate the given compositions. <IMAGE>

g(h(ƒ(4)))