3. Functions

Use the graphs of f and g to evaluate each composite function.

(go f) (0)

Find the domain of each function. h(x) = 4/(3/x - 1)

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

$(g\circ \text{ƒ})(-2)$

In Exercises 39-52, a. Find an equation for ƒ¯¹(x). b. Graph ƒ and ƒ¯¹(x) in the same rectangular coordinate system. c. Use interval notation to give the domain and the range of f and ƒ¯¹. ƒ(x) = x² − 4, x ≥ 0

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

Use the definition of inverses to determine whether ƒ and g are inverses. f(x) = 2/(x+6), g(x) = (6x+2)/x

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

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

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

(ƒ+g)(2)

Use the table to evaluate each expression, if possible.

$\left(f/g\right)\left(0\right)$

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

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

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

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

Let ƒ(x)=2x-3 and g(x)=-x+3. Find each function value. (g∘ƒ)(0)

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

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

Find ƒ+g and determine the domain for each function.

f(x)= = (5x+1)/(x² - 9), g(x) = (4x -2)/(x² - 9)

Find ƒ+g, ƒ- g, ƒg and ƒ/g. Determine the domain for each function. f(x) = 2x² − x − 3, g (x) = x + 1