contestada

Let f be differentiable such that f(-2)=3,f(3)=5, f'(-2)=4 and f'(3)=6. Let g be differentiable functions such that g(x)=f^-1 (x) for all x. What is the value of g'(3)

Respuesta :

ajdonis

Answer:

[tex]g'(3)=\frac{1}{4}[/tex]

Step-by-step explanation:

There is a rule in calculus that tells us that:

[tex]g'[f(x)]=\frac{1}{f'(x)}[/tex]

In this case, we know that f(-2)=3, therefore:

g'(3)=g'(f(-2))

So, if we used the rule, we would get that:

[tex]g'[f(-2)]=\frac{1}{f'(-2)}[/tex]

we know that f'(-2)=4, so:

[tex]g'[f(-2)]=\frac{1}{4}[/tex]

or:

[tex]g'[3]=\frac{1}{4}[/tex]

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