Computation of images and inverse images
Consider the function $f$ defined by three plus the root of a given real number. Find its analytical expression as well as $f (1), f (4)$ and $f^{-1}(7)$.
We write the algebraic expression of the function:
$$f(x)=\sqrt{x}+3$$
We can calculate now: $$f(1)=\sqrt{1}+3=1+3=4$$ $$f(4)=\sqrt{4}+3=2+3=5$$ $$f^{-1}(7):$$ $$7=\sqrt{x}+3$$ $$4=\sqrt{x}$$ $$x=16$$
$$f(x)=\sqrt{x}+3$$
$$f(1)=4$$
$$f(4)=5$$
$$f^{-1}(7)=16$$