Some function questions

1.

Let $f(x) = 4x - 7$, $g(x) = (x + 1)^2$, and $s(x) = f(x) + g(x)$. What is $s(3)$?

2.

Suppose $a(x) = 3x - 7$ and $b(x) = 2 - x^3$. Find $a(b(3)) - b(a(3))$.

3.

Let $f(x) = 2x^2 + 3x - 9,$ $g(x) = 5x + 11,$ and $h(x) = -3x^2 + 1.$ Find $f(x) - g(x) + h(x).$

4.

Let $f(x) = 3x + 2$ and $g(x) = x^2 - 5x - 1.$ Find $f(g(x)).$

5.

Let $f(x) = \frac{2}{\sqrt{x}}$. What is the domain of $f$? Express your answer with interval notation

6.

Let $f(x) = \dfrac{2-3x}{5-2x}$. For what value of $a$ is $f(a) = 3$?

7.

Let $f(x) = 3(x - 6)^2 + 1$. What is the range of $f$? Express your answer with interval notation.

8.

The function $f(x)$ satisfies $$f(\sqrt{x + 1}) = \frac{1}{x}$$ for all $x \ge -1,$ $x\neq 0.$ Find $f(2)$.

9.

Let $f(x) = 3x^2 - 4x$. Find the constant $k$ such that  $f(x) = f(k - x)$ for all real numbers $x$.