3. Functions

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h. ƒ(x)=1/x

Find ƒ+g, f−g, fg, and f/g. Determine the domain for each function. f(x) = √(x -2), g(x) = √(2-x)

Find

a. (fog) (x)

b. (go f) (x)

c. (fog) (2)

d. (go f) (2).

f(x) = 2x, g(x) = x+7

Find

a. (fog) (x)

b. (go f) (x)

c. (fog) (2)

d. (go f) (2).

f(x) = x+4, g(x) = 2x + 1

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4.

$\text{ƒ}\left(x\right)=1-x^2$

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h. ƒ(x)=x²+3x+1

Find a. (fog) (2) b. (go f) (2) f(x)=4x-3, g(x) = 5x² - 2

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

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

$(\text{ƒ}\circ g)(-2)$

Find a. (fog) (2) b. (go f) (2) f(x) = 4-x, g(x) = 2x² +x+5

Find a. (fog) (x) b. (go f) (x) f(x) = 4-x, g(x) = 2x² +x+5

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

Find c. (fog) (2) d. (go f) (2). f(x) = √x, g(x) = x − 1

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