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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

Unit 8.1 Printable Copy

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