Question

If f(x) = square root of x+3, what is the equation for f–1(x)? f–1(x) = x2 - 3 f–1(x) = x2 + 3 f–1(x) = (x - 3) 2 f–1(x) = (x + 3) 2

Answer 1

`\Large \boxed{\sf \ \ f^(-1)(x)=x^2-3 \ \ }`

Explanation:

Hello,

`\text{For }x+3\geq 0\\\\f(x)=√(x+3)\\\\x=(fof^(-1))(x)=f(f^(-1)(x))=\sqrt{f^(-1)(x)+3}\\\\\text{*** take the square ***}\\\\f^(-1)(x)+3=x^2\\\\\text{*** subtract 3 from both sides ***}\\\\\large \boxed{\sf \ \ f^(-1)(x)=x^2-3 \ \ }\\`

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