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 $$f^{-1}(7)$$.
See development and solution
Development:
We write the algebraic expression of the function:
$$$f(x)=\sqrt{x}+3$$$
We can calculate now: $$$f(1)=\sqrt{1}+3=1+3=4$$$ $$$f(4)=\sqrt{4}+3=2+3=5$$$ $$$f^{-1}(7):$$$ $$$7=\sqrt{x}+3$$$ $$$4=\sqrt{x}$$$ $$$x=16$$$
Solution:
$$f(x)=\sqrt{x}+3$$
$$f(1)=4$$
$$f(4)=5$$
$$f^{-1}(7)=16$$