3. Functions

Let ƒ(x)=2x-3 and g(x)=-x+3. Find each function value. See Example 5.

$(\text{ƒ}\circ \text{ƒ})\left(2\right)$

Find a. (fog) (x) b. (go f) (x) c. (fog) (2) d. (go f) (2).

f(x) = 2x-3, g(x) = (x+3)/2

Find a. (fog) (x) b. the domain of f o g.

f(x) = √x, g(x) = x − 2

Find a. (fog) (x) b. the domain of f o g.

f(x) = x² + 4, g(x) = √(1 − x)

Given functions f and g, (b)$(g\circ \text{ƒ})\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=-6x+9,g\left(x\right)=5x+7$

Given functions f and g, find (a)$(\text{ƒ}\circ g)\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=8x+12,g\left(x\right)=3x-1$

Express the given function h as a composition of two functions ƒ and g so that h(x) = (fog) (x).

h(x) = (3x − 1)⁴

Given functions f and g, find (a)$(\text{ƒ}\circ g)\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=x^3,g\left(x\right)=x^2+3x-1$

Given functions f and g, (b)$(g\circ \text{ƒ})\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=x^3,g\left(x\right)=x^2+3x-1$

Given functions f and g, find (b)$(g\circ \text{ƒ})\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=x+2,g\left(x\right)=x^4+x^2-4$

Given functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=\text{√}(x-1),g\left(x\right)=3x$

Given functions f and g, find (a)(ƒ∘g)(x) and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=\text{√}(x-1),g\left(x\right)=3x$

Express the given function h as a composition of two functions ƒ and g so that h(x) = (fog) (x).

h(x) = 1/(2x-3)

Given functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=\frac{2}{x},g\left(x\right)=x+1$

Given functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=\surd (x+2),g\left(x\right)=-\left(\frac{1}{x}\right)$