Solving equations involving composite functions

12 questions

1. {\text{fg}}(x), {\text{fgh}}(x), and {\text{fff}}(x) are all examples of __________.
2. If {\text{f}}(x)=7x−4 and {\text{g}}(x)=3x evaluate {\text{gf}}(11).
3. Solve 4(x-3)=22 x=___.
4. If {\text{f}}(x)=6x−15 solve {\text{f}}(x)=57 x=___.
5. If {\text{f}}(x)=7x−4 and {\text{g}}(x)=3x which is an expression for {\text{gf}}(x)?
6. Solve 3x^2+3=150.
7. For the function {\text{fg}}(x) the x values are in the domain and the values of {\text{fg}}(x) are in the __________.
8. If {\text{f}}(x)=3x and {\text{g}}(x)=2x+9 solve {\text{fg}}(x)=-3 x=___.
9. If {\text{f}}(x)=3x and {\text{g}}(x)=2x+9 solve {\text{gf}}(x)=-3 x=___.
10. If {\text{f}}(x)=3x and {\text{g}}(x)=2x+9 solve {\text{fg}}(x)={\text{gf}}(x).
11. If {\text{f}}(x)=2x-7 what do you notice when we solve {\text{f}}(x)={\text{f}}^{-1}(x)?
12. If {\text{f}}(x)=7-2x and {\text{g}}(x)=x^2 solve {\text{gf}}(x)=9.

License: OGL