f ⁻¹( x)= x^2+4 is the inverse of f(x)= [tex]\sqrt{x-4}[/tex]
what is an inverse function ?
An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by 'f' or 'F', then the inverse function is denoted by f-1 or F-1.
write f(x)= [tex]\sqrt{x-4}[/tex] as an equation
y= [tex]\sqrt{x-4}[/tex]
interchange the variables
x= [tex]\sqrt{y-4}[/tex]
solve the equation for y we get
squaring both side ,we have
x^2 = y-4
this implies that
y= x^2 +4
replace y with f ⁻¹( x) to show the final answer
f ⁻¹( x)= x^2+4
Hence, f ⁻¹( x)= x^2+4 is the inverse of f(x)= [tex]\sqrt{x-4}[/tex]
learn more about of inverse function here
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