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2 years ago

F(x)=x^2-6. find the inverse

Mathematics

2 answers:

VLD [36.1K]2 years ago

6 0

Hi :)

Let's find the inverse of the function

Remember, inverse functions do the opposite things in the opposite order.

To find the inverse,

replace $\boldsymbol{f(x)}$ with $\boldsymbol{y}$
swap x's and y's
solve for y

Replace f(x) with y. (one step)

Then

$\boldsymbol{y=x^2+6}$

Swap x's and y's (one step)

Then

$\boldsymbol{x=y^2+6}$

Solve for y (several steps)

$\boldsymbol{x-6=y^2}$ > square root both sides

$\boldsymbol{\sqrt{x-6}=y}$ > swap y and √x-6

$\boldsymbol{y=\sqrt{x-6}}$

$\tt{Learn~More;Work~Harder}$

:)

OlgaM077 [116]2 years ago

4 0

Answer:

f-1(x) = +- sqrt(x + 6)

Step-by-step explanation:

f(x) = x^2 - 6

y = x^2 - 6

x = y^2 - 6

x + 6 = y^2

y = +- sqrt(x + 6)

f-1(x) = +- sqrt(x + 6)

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From the homogeneous part of the ODE, we can get two fundamental solutions. The characteristic equation is

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