Answered

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Consider the function.f(x) = x2 − 1, x ≥ 1

Consider The Functionfx X2 1 X 1 class=

Sagot :

t Given

[tex]f(x)=\sqrt{x^2-1}[/tex]

Find

inverse of f(x)

domain and range of function and its inverse

Explanation

Let y = f(x)

[tex]y=\sqrt{x^2-1}[/tex]

replace all x with y and y with x

[tex]x=\sqrt{y^2-1}[/tex]

now solve for y

[tex]\begin{gathered} \sqrt{y^2-1}=x \\ y^2-1=x^2 \\ y^2=x^2+1 \\ y=\pm\sqrt{x^2+1} \end{gathered}[/tex]

so, the inverse is

[tex]\pm\sqrt{x^2+1}[/tex]

domain of f(x) is

[tex]x\epsilon R:x\leq-1\text{ or x}\ge1[/tex]

range of f(x) is

[tex]y\epsilon R:y\ge0[/tex]

domain of inverse is

[tex]R[/tex]

range of inverse function is

[tex]y\epsilon R:y\ge1[/tex]
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