# Composition of Functions Worksheet

Composition of Functions Worksheet
• Page 1
1.
State the domain of [$f$ o $g$]($x$) for $f$($x$) = and $g$($x$) = $x$ + 1.
 a. $x$ ≥ 1 b. $x$ ≥ 0 c. $x$ ≥ 2 d. $x$ ≥ 3

2.
State the domain of [$f$ o $g$]($x$) for $f$($x$) = 2$x$ + 4 and $g$($x$) = $\frac{1}{x}$.
 a. $x$ ≠ 0 b. $x$ ≤ 4 c. $x$ ≥ 2 d. $x$ = 0

3.
State the domain of [$f$ o $g$]($x$) for $f$($x$) = $\frac{1}{x}$ and $g$($x$) = 2$x$ + 4.
 a. $x$ = $\frac{1}{2}$ b. $x$ ≥ 2 c. $x$ ≠ - 2 d. $x$ = - 2

4.
Find the domain of [$f$ o $g$]($x$) for $f$($x$) = (${x}^{2}$ - 1)and $g$($x$) = $\sqrt{x}$.
 a. (- ∞, - 1] ∩ [1, ∞) b. [ 0, ∞) c. (- ∞, - 1] ∪ [1, ∞) d. (0, 1)

5.
State the domain of [$f$ o $g$]($x$) for $f$($x$) = and $g$($x$) = $x$ + 1.
 a. $x$ ≥ 2 b. $x$ ≤ 3 c. $x$ ≤ 2 d. $x$ ≥ 3

6.
Evaluate the composite function ($f$o$g$)($x$), given $f$($x$) = 4$x$ + 6 and $g$($x$) = $x$ - 9.
 a. 4$x$ - 54 b. 4$x$ - 3 c. 4$x$ - 30 d. 4$x$2 - 30$x$ - 54

7.
If $f$($x$) = 3$x$2 and $g$($x$) = 5$x$ + 2, then find ($g$o$f$)($x$).
 a. 15$x$3 + 6$x$2 b. 15$x$ + 6 c. 6$x$2 d. 15$x$2 + 2

8.
If $f$($x$) = 2$x$ + 4 and $g$($x$) = 5$x$2, evaluate the composite function ($f$o$g$)($x$2).
 a. (10$x$2 + 4)2 b. 10$x$2 + 4 c. 10$x$4 + 4 d. (10$x$ + 4)2

9.
If $f$($x$) = 5$x$ - 9 and $g$($x$) = 5$x$3, find the value of the composite function ($g$o$f$)(3$x$).
 a. $x$3 - 15 b. (15$x$ - 27)3 c. 15($x$3 - 5) d. 5(15$x$ - 9)3

If $f$($x$) = - 2$x$4 and $g$($x$) = 4$x$ - 6, then find ($f$o$g$)($x$ - 1).
 a. 2(4$x$ - 6)4 - 1 b. - 4($x$ - 1)4(2$x$ - 5) c. - 2($x$4 - 1) d. - 2(4$x$ - 10)4