3. Functions

Use the tables for ƒ and g to evaluate each expression.

$(\text{ƒ}\circ g)\left(3\right)$

Given functions f and g, find (a)(ƒ∘g)(x) and its domain, and (b)(g∘ƒ)(x) and its domain. ƒ(x)=1/(x+4), g(x)=-(1/x)

Find a. (fog) (2) b. (go f) (2) f(x) = x²+2, g(x) = x² – 2

Without using paper and pencil, evaluate each expression given the following functions. $\text{ƒ}\left(x\right)=x+1$ and $g\left(x\right)=x^2$

$\left(\text{ƒ}/g\right)\left(2\right)$

Use the graph to evaluate each expression. See Example 3(a). 

(ƒ+g)(0)

Find the inverse of each function that is one-to-one. {(3,-1), (5,0), (0,5), (4, 2/3)}

For the pair of functions defined, find (ƒ+g)(x). Give the domain of each. See Example 2.

ƒ(x)=√(4x-1), g(x)=1/x

Determine whether each function graphed or defined is one-to-one. y = 2x - 8

Without using paper and pencil, evaluate each expression given the following functions. $\text{ƒ}\left(x\right)=x+1$ and $g\left(x\right)=x^2$

$(\text{ƒ}+g)\left(2\right)$

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

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

In Exercises 53–58, f and g are defined by the following tables. Use the tables to evaluate each composite function. (go f) (-1)

Find f/g and determine the domain for each function. f(x) = 2x + 3, g(x) = x − 1

Find fg and determine the domain for each function. f(x)= = 8x/(x - 2), g(x) = 6/(x+3)

Let $\text{ƒ}\left(x\right)=3x^2-4$ and $g\left(x\right)=x^2-3x-4$. Find each of the following.

$(f+g)\left(2k\right)$

Let f(x) = 2x - 5 g(x) = 4x - 1 h(x) = x² + x + 2. Evaluate the indicated function without finding an equation for the function. ƒ^-1 (1)