Hi Keith;
f(x)=3/(x4)
The denominator cannot equal zero. The domain is from negative infinity to positive infinity except for that which corresponds to...
x4=0
x=4
(infinity, 4)U(4, +infinity)
Because the results of this equation can never be zero, the range is...
(infinity, 0)U(0, +infinity)
f^{1}(x)=
y=3/(x4)
Let's isolate x...
Let's crossmultiply...
y(x4)=3
Let's divide both sides by y...
[y(x4)]/y=3/y
x4=3/y
Let's add 4 to both sides...
x4+4=(3/y)+4
x=(3/y)+4
Let's switch x and y...
y=(3/x)+4
f^{1}(x)=(3/x)+4
Domain is...
(infinity, 0)U(0, +infinity)
Because the denominator x cannot equal zero, f^{1}(x) cannot result in 4.
Range is...
(infinity, 4)U(4, +infinity)
Feb 10

Vivian L.
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