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f(x)=3√x + 7. Find the inverse of f(x).

Sagot :

Dabossbidn
f(x)=(x^2-14x+49)/9


step 1- switch x and y
step 2- isolate y, and get to (x-7)/3=sqrty
step 3- square each side to get rid of the square root and isolate y
step 4- f(x)=(x^2-14x+49)/9
Semsee45idn

Answer:

[tex]f^{-1}(x)=\left(\dfrac{x-7}{3}\right)^2[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=3\sqrt{x}+7[/tex]

To find the inverse of the function

Swap f(x) for y:

[tex]\implies y=3 \sqrt{x}+7[/tex]

Subtract 7 from both sides:

[tex]\implies y-7=3 \sqrt{x}+7-7[/tex]

[tex]\implies y-7=3\sqrt{x}[/tex]

Divide both sides by 3:

[tex]\implies \dfrac{3\sqrt{x}}{3}=\dfrac{y-7}{3}[/tex]

[tex]\implies \sqrt{x}=\dfrac{y-7}{3}[/tex]

Square both sides:

[tex]\implies \left(\sqrt{x}\right)^2=\left(\dfrac{y-7}{3}\right)^2[/tex]

[tex]\implies x=\left(\dfrac{y-7}{3}\right)^2[/tex]

Swap the x for [tex]f^{-1}(x)[/tex] and y for x:

[tex]\implies f^{-1}(x)=\left(\dfrac{x-7}{3}\right)^2[/tex]

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