8.1 Homework Problems: Functions and Inverse Functions
1. Compute the following if f(x) = 2x + 1
a. f(4)
b. f(0)
c. f(-1)
2. Compute the following if f(x) = 4x and g(x) = x + 5
a. find (f · g)(x)
b. find (f ◦ g) (x)
c. find (g ◦ f) (x)
3. find h(a(m)) if h(m) = 2m + 1 and a(m) = 9m2 + 4
4. find (g ◦ f) (1) if f(x) = 2x + 5 and [latex]g(x)\ =\ \frac{x\ -\ 5}{2}[/latex]
5. Find (f – h)(x) if f(x) = 3x2 and h(x) = x2
6. Find [latex]\frac{f}{g}(x)[/latex] if f(x) = 2x + 3 and g(x) = 5x – 6 then evaluate for x = -2
7. Find (f ◦ g)(x) and (g ◦ f)(x) if f(x) = x2 – 4x +1 and g(x) = 2x – 4
8. Find (f ◦ g)(x) and (g ◦ f)(x) if f(x) = x2 + 4 and g(x) = [latex]\sqrt{x\ -\ 3}[/latex]
9. Given the function f(x) = 3x2 + 4x + 1 find the following values
a. f(w)
b. f(z +1)
c. f(3b – 1)
d. f(-b + 2)
10. Graph the function and determine if it is one to one using the horizontal line test
a. [latex]f(x)\ =\ \sqrt{x\ +\ 5}[/latex]
b. [latex]g(x)\ =\ -x^2+1[/latex]
11. Find the inverse of the function f(x) = 3x – 4
12. Find the inverse of the function g(x) = [latex]\frac{1}{2}[/latex]x + 5
13. Are these two functions inverses of each other?
a. [latex]f(x)\ =\ \frac{x}{4}[/latex] and g(x) = 4x
b. g(x) = [latex]\frac{x+7}{5}[/latex] and h(x) = 5x + 7