15.1 Functions: inverse and composite — Practise

1. Find the inverse of $f(x)=3x+5$.

Answer: $\frac{x-5}{3}$

2. Find the inverse of $f(x)=4x-7$.

Answer: $\frac{x+7}{4}$

3. Find the inverse of $f(x)=\frac{x-2}{5}$.

Answer: $5x+2$

4. Let $f(x)=2x+1$ and $g(x)=x^2$. Find $f(g(x))$.

Answer: $2x^2+1$

5. Let $f(x)=2x+1$ and $g(x)=x^2$. Find $g(f(x))$.

Answer: $(2x+1)^2$

6. Let $f(x)=x-4$ and $g(x)=3x$. Find $f(g(x))$.

Answer: $3x-4$

7. Let $f(x)=x-4$ and $g(x)=3x$. Find $g(f(x))$.

Answer: $3x-12$

8. State the excluded value for $h(x)=\frac{1}{x+6}$.

Answer: $x\neq-6$

9. For $f(x)=2x+3$ and $g(x)=\frac{x-3}{2}$, simplify $g(f(x))$.

Answer: $x$

10. For $f(x)=2x+3$ and $g(x)=\frac{x-3}{2}$, simplify $f(g(x))$.

Answer: $x$