Composition and inverses by hand

Medium0 of 10 parts

Ten questions on running functions one after another and on running them backwards. Type sqrt(x) for a square root, and give rules in terms of $x$ .

For every inverse you find, check it in your head by sending one number through and back before typing the answer.

With $f(x) = 2x + 3$ and $g(x) = x^2$ , find $(f \circ g)(2)$ .

With the same two functions, find $(g \circ f)(2)$ .

With $f(x) = 2x + 3$ and $g(x) = x^2$ , write $f(g(x))$ in terms of $x$ .

in terms of x

With the same two functions, write $g(f(x))$ in terms of $x$ .

in terms of x

Find the inverse of $f(x) = 3x - 4$ , in terms of $x$ .

in terms of x

Find the inverse of $f(x) = \dfrac{x - 1}{2}$ , in terms of $x$ .

in terms of x

The function $f(x) = x^2$ is restricted to $x \ge 0$ . Write its inverse in terms of $x$ .

in terms of x

With $f(x) = 5x - 2$ and $g(x) = \dfrac{x + 2}{5}$ , find $f(g(7))$ .

Find the inverse of $f(x) = 4 - x$ , in terms of $x$ .

in terms of x

With $f(x) = 3x - 4$ , find $f^{-1}(10)$ .