Question

if f(x)=√ 2x+5, find the value of f^-1(5)


help me pleaaasee :D

Answer 1

f^-1(5) means f(x) = 5

Answer 2

you're given f(x). Just find x

Answer 3

doesnt f^-1 mean the inverse?

Answer 4

so like the inverse of f(x) when f(x)=5? :/

Answer 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"

Answer 6

ok, but what does the (5) part do? if anything?

Answer 7

well, first off, find the inverse

Answer 8

then once you find that, you'd use the 5 in it

Answer 9

is it y=x^2-5 all over 2?

Answer 10

yeap, so \(\bf f(x)={\color{red}{ y}}=\sqrt{2{\color{blue}{ x}}+5}\qquad inverse\implies {\color{blue}{ x}}=\sqrt{2{\color{red}{ y}}+5}
\\ \quad \\
\cfrac{{\color{blue}{ x}}^2-5}{2}=y=f^{-1}({\color{blue}{ x}})\qquad f^{-1}({\color{blue}{ 5}})=\cfrac{{\color{blue}{ 5}}^2-5}{2}\)

Answer 11

10

Answer 12

yeap

Answer 13

yay, do u mind helping me with another question?

Answer 14

ok

Answer 15

write a quadratic inequality for which the solution is -2<x<5