Since f(x) is (strictly) increasing, we know that it is one-to-one and has an inverse f^(-1)(x). Then we can apply the inverse function theorem. Suppose f(a) = b and a = f^(-1)(b). By definition of inverse function, we have
f^(-1)(f(x)) = x
Differentiating with the chain rule gives
(f^(-1))'(f(x)) f'(x) = 1
so that
(f^(-1))'(f(x)) = 1/f'(x)
Let x = a; then
(f^(-1))'(f(a)) = 1/f'(a)
(f^(-1))'(b) = 1/f'(a)
In particular, we take a = 2 and b = 7; then
(f^(-1))'(7) = 1/f'(2) = 1/5
3x-195>=5x-21
Add 21 to both sides
3x-174>5x
Sub 3x from both sides
-174>2x
Divide both sides by 2
-87>x
I can’t see the question (picture is blurry)
Answer:
The last one or b(32-16)
Step-by-step explanation:
Because when simplified it is b times 32 minus 16b
or
32b-16b
Answer:
9x - 4y = 55
Step-by-step explanation:
The equation for the perpendicular line can be written by swapping the x- and y-coefficients and negating one of them. Usually we choose to negate the one that makes the x-coefficient positive. Here, that process gives ...
9x - 4y = <some constant>
The value of the constant can be found by putting the (x, y) values of the given point into the left-side expression:
9x - 4y = 9·7 -4·2 = 55
9x - 47 = 55