Answered

Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

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

Sagot :

dabossb
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
semsee45

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]

We hope this was helpful. Please come back whenever you need more information or answers to your queries. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.