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1 vote

f(x) = {x}^(2) - 4

for all instances of

x \leqslant 0
a) show that f has an inverse function

{f}^(- 1)
b) find

dom( {f}^( - 1) ) \: and \: ran( {f}^( - 1) )
c) find

{f}^( - 1) (x)



User Eirini
by
7.2k points

1 Answer

3 votes

Given function
f(x)=x^2-4 find its inverse by substituting x for f(x) and then solving for f(x).


x=f(x)^2-4\implies f(x)^(-1)=√(x+4)

Where
x+4>=0 for x to be real.

So solve the inequality and you will obtain the domain:


x+4>=0\implies x>=-4\implies x\in[-4,+\infty).

Range is equal to the range of square root function,


y\in[0, +\infty).

Hope this helps.

User Danny Mencos
by
5.9k points
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