Composite Functions

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Show your work for each problem.

1.
If $f(x) = x + 2$ and $g(x) = 3x$ , what is $(f \circ g)(1)$ ?
1. a)4
2. b)9
3. c)5
4. d)6
2.
What does $(f \circ g)(x)$ mean?
1. a) $f(x) + g(x)$
2. b) $g(f(x))$
3. c) $f(g(x))$
4. d) $f(x) \cdot g(x)$
3.
If $f(x) = x^2$ and $g(x) = x + 1$ , find $(f \circ g)(2)$ .
4.
If $f(x) = 2x$ and $g(x) = x - 3$ , find $(g \circ f)(4)$ .
5.
If $f(x) = x + 5$ and $g(x) = 2x$ , find $(f \circ g)(3)$ .
6.
If $f(x) = x^2$ and $g(x) = x + 3$ , what is $(f \circ g)(x)$ ?
1. a) $x^2 + 9$
2. b) $x^2 + 3$
3. c) $(x + 3)^2$
4. d) $x^3 + 3x^2$
7.
If $f(x) = 3x - 1$ and $g(x) = x + 4$ , find $(f \circ g)(2)$ .
8.
If $f(x) = x^2$ and $g(x) = 2x + 1$ , find $(g \circ f)(3)$ .
9.
If $f(x) = 2x - 3$ and $g(x) = x^2$ , find the formula for $(f \circ g)(x)$ .
10.
If $f(x) = x - 1$ and $g(x) = 4x$ , compare $(f \circ g)(2)$ and $(g \circ f)(2)$ . Are they equal?
11.
Which statement about function composition is true?
1. a)In $(f \circ g)(x)$ , $f$ is applied first
2. b) $(f \circ g)(x)$ and $(g \circ f)(x)$ can be different
3. c) $(f \circ g)(x) = (g \circ f)(x)$ for all functions $f$ and $g$
4. d) $(f \circ g)(x) = f(x) \cdot g(x)$
12.
If $f(x) = \sqrt{x}$ and $g(x) = x + 9$ , find $(f \circ g)(7)$ .
13.
If $f(x) = 3x + 2$ , $g(x) = x - 1$ , and $h(x) = x^2$ , find $(f \circ g \circ h)(2)$ .
14.
If $f(x) = x + 2$ and $g(x) = 3x - 5$ , find $(g \circ f)(x)$ as a simplified expression.
15.
If $f(x) = x^3$ and $h(x) = (2x - 1)^3$ , find $g(x)$ so that $h(x) = (f \circ g)(x)$ .
16.
If $f(x) = \frac{1}{x}$ and $g(x) = x + 2$ , what is $(f \circ g)(3)$ ?
1. a) $5$
2. b) $\frac{1}{5}$
3. c) $\frac{5}{3}$
4. d) $\frac{1}{3}$