Question

Evaluate f(3)-f^-1(5)-2f^-1(3)

Answer 1

I don’t have f given, so I can’t compute a numeric value. Do you mean f^-1 as the inverse function? If so, to evaluate

f(3) − f⁻¹(5) − 2f⁻¹(3)

you need:
- f(3) directly,
- the number a such that f(a)=5 (then a = f⁻¹(5)),
- the number b such that f(b)=3 (then b = f⁻¹(3)).

So the value is f(3) − a − 2b, where a solves f(a)=5 and b solves f(b)=3.

If you give the definition of f I will compute it. For example, if f(x)=2x+1 then f⁻¹(x)=(x−1)/2, so
- f(3)=7,
- f⁻¹(5)=(5−1)/2=2,
- f⁻¹(3)=(3−1)/2=1,

and the expression equals 7 − 2 − 2·1 = 3.

If f is linear f(x)=ax+b (a≠0) the expression simplifies to
3a + b − (5−b)/a − 2(3−b)/a = 3a + b − (11 − 3b)/a.

Tell me f(x) and I’ll evaluate it.