3. Functions

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. ƒ(x)=1+2x^2

In Exercises 51–66, find a. (fog) (x)b. (go f) (x) f(x)=4x-3, g(x) = 5x² - 2

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. ƒ(x)=x^2-4x+2

In Exercises 51–66, find a. (fog) (2)b. (go f) (2) f(x) = 4-x, g(x) = 2x² +x+5

Let ƒ(x)=2x-3 and g(x)=-x+3. Find each function value. See Example 5. (g∘ƒ)(0)

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

In Exercises 51–66, find a. (fog) (x)b. (go f) (x)c. (fog) (2)d. (go f) (2). f(x) = 1/x, g(x)= 1/x

Given functions f and g, find (a)(ƒ∘g)(x) and its domain. See Examples 6 and 7. ƒ(x)=8x+12, g(x)=3x-1

Given functions f and g, find (a)(ƒ∘g)(x) and its domain. See Examples 6 and 7. ƒ(x)=√x, g(x)=x+3

In Exercises 75-82, 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, (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7. ƒ(x)=x^3, g(x)=x^2+3x-1

Given functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7. ƒ(x)=x+2, g(x)=x^4+x^2-4

Given functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7. ƒ(x)=√(x-1), g(x)=3x

Use the graphs of f and g to solve Exercises 83–90.

Find (g-f) (-2).

Given functions f and g, find (a)(ƒ∘g)(x) and its domain. See Examples 6 and 7. ƒ(x)=√x, g(x)=1/(x+5)