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What is the inverse of f(x)=2x−3 ?

What is the inverse of the function?
f(x)=4x+10

What is the inverse of f(x)=x4+7 for x≥0 where function g is the inverse of function f?

Respuesta :

dencsid
The inverse of f(x)=2x−3 is f(x)=(x+3)/2, the inverse of the function f(x)=4x+10 is f(x)=(x-10)/4. 
The 3rd question is not clear. What is x4 and where is the function g?

Answer and Explanation :

We have to find the inverse of the functions below :

1) [tex]f(x)=2x-3[/tex]

Let f(x)=y

[tex]y=2x-3[/tex]

Replace the value of x and y,

[tex]x=2y-3[/tex]

Now we find y,

[tex]x+3=2y[/tex]

[tex]y=\frac{x+3}{2}[/tex]

The inverse of the function is [tex]f^{-1}(x)=\frac{x+3}{2}[/tex]

2) [tex]f(x)=4x+10[/tex]

Let f(x)=y

[tex]y=4x+10[/tex]

Replace the value of x and y,

[tex]x=4y+10[/tex]

Now we find y,

[tex]x-10=4y[/tex]

[tex]y=\frac{x-10}{4}[/tex]

The inverse of the function is [tex]f^{-1}(x)=\frac{x-10}{4}[/tex]

3) [tex]f(x)=x^4+7[/tex] for x≥0

Let f(x)=y

[tex]y=x^4+7[/tex]

Replace the value of x and y,

[tex]x=y^4+7[/tex]

Now we find y,

[tex]x-7=y^4[/tex]

[tex]y=(x-7)^{\frac{1}{4}}[/tex]

The inverse of the function is [tex]g(x)=(x-7)^{\frac{1}{4}}[/tex]

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