Let f(X)= 2x^2+x+1 , with x=-1/4. Find the slope of the tangent line to the graph of y= f^(-1) (X) { f inverse of x } @ x =4

Question

Let f(X)= 2x^2+x+1 , with x>=-1/4. Find the slope of the tangent line to the graph of y= f^(-1) (X) { f inverse of x } @ x =4

anonymous · Answer

do i first set my equation >= to -1/4 and solve it

ganeshie8 · Answer

you wanto find the slope at x = 4 for f^-1(x)

anonymous · Answer

ya

ganeshie8 · Answer

since 4 is x-coordinate of f^-1(x), 4 will be y-coordinate of f(x). 
lets find teh corresponding x-coordinate of f(x) :-

4 = 2x^2 + x + 1

ganeshie8 · Answer

By inspection x = 1
thus, (1, 4) is a point on f(x), which forces (4, 1) to be a point on f^-1(x)

ganeshie8 · Answer

next find $f'(1)$ :-

$f(x) =  2x^2+x+1$
$f'(x) =  4x+1$

$f'(1) = 4(1) + 1 = 5$

ganeshie8 · Answer

$\large  f^{-1}(4) = \frac{1}{f'(1)} = \frac{1}{5} = 0.2$

see if that makes more or less sense

ganeshie8 · Answer

anonymous · Answer

but where did we use -1/4

ganeshie8 · Answer

good question :)

ganeshie8 · Answer

you need to look at graph, to *understand* why the constrain x >= -1/4 is given.
let me show u quick

ganeshie8 · Answer

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