if f(x)=√ 2x+5, find the value of f^-1(5) help me pleaaasee :D
f^-1(5) means f(x) = 5
you're given f(x). Just find x
doesnt f^-1 mean the inverse?
so like the inverse of f(x) when f(x)=5? :/
\(\bf f(x)={\color{red}{ y}}=\sqrt{2{\color{blue}{ x}}+5}\qquad inverse\implies {\color{blue}{ x}}=\sqrt{2{\color{red}{ y}}+5}\) solve for "y" notice that to find the inverse, all we do is swap about the variables, then solve for "y"
ok, but what does the (5) part do? if anything?
well, first off, find the inverse
then once you find that, you'd use the 5 in it
is it y=x^2-5 all over 2?
yeap, so \(\bf f(x)={\color{red}{ y}}=\sqrt{2{\color{blue}{ x}}+5}\qquad inverse\implies {\color{blue}{ x}}=\sqrt{2{\color{red}{ y}}+5} \\ \quad \\ \cfrac{{\color{blue}{ x}}^2-5}{2}=y=f^{-1}({\color{blue}{ x}})\qquad f^{-1}({\color{blue}{ 5}})=\cfrac{{\color{blue}{ 5}}^2-5}{2}\)
10
yeap
yay, do u mind helping me with another question?
ok
write a quadratic inequality for which the solution is -2<x<5
Join our real-time social learning platform and learn together with your friends!