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Grade 12 Maths problem?
Hi, I have an assignment due tomorrow and am having difficulty with several questions. Can anyone help? Thanks very much, if you can
(c) Given: f(x) = 3x, find a simplified expression for
f(x) + f(1/x) + 1/f(x) + f^-1(x)
and
Given y = x^3 – x^2 – x + 2
1. Find the equation of the tangent to the curve at the point where x = -1 : I got the answer for this one, which is y = 4x + 5
The second part, however, I have no idea how to do:
2. Find the x-coordinate of another point on the curve at which the tangent is parallel to the one found in (1)
2 Answers
- DylanLv 51 decade agoFavorite Answer
f(x) = 3x
f(1/x) = 3(1/x) = 3/x
1/f(x) = 1/(3x)
For f-1(x)
y = 3x
x = 3y
y = x/3
f-1(x) = x/3
Add them together
= 3x + 3/x + 1/(3x) + x/3
= 10x/3 + 10/(3x)
1. f(x) = y = x^3 - x^2 - x + 2
f'(x) = y' = 3x^2 - 2x - 1
f'(-1) = 3(-1)^2 - 2(-1) - 1 = 4
f(-1) = (-1)^3 - (-1)^2 - (-1) + 2 = 1
y - 1 = 4(x + 1)
y = 4x + 5
2. Since the tangent line is parallel, it has the same slope
f'(x) = 3x^2 - 2x - 1 = 4
Solve for x
3x^2 - 2x - 5 = 0
3x^2 + 3x - 5x - 5 = 0
(3x - 5)(x + 1) = 0
x = -1, or x = 5/3
