Suppose that f(x) is an invertible function (that is, has an inverse function), and that the slope of the tangent line to the curve y = f(x) at the point (2, –4) is –0.2. Then:
(Points : 1)
A) The slope of the tangent line to the curve y = f –1(x) at the point (–4, 2) is –0.2.
B) The slope of the tangent line to the curve y = f –1(x) at the point (2, –4) is –5.
C) The slope of the tangent line to the curve y = f –1(x) at the point (2, –4) is 5.
D) The slope of the tangent line to the curve y = f –1(x) at the point (–4, 2) is –5.
E) The slope of the tangent line to the curve y = f –1(x) at the point (–4, 2) is 5.
Looks like D to me
The ans is D
Are you possibly Steve Hawkins? Your getting this one after another.
E) The slope of the tangent line to the curve y = f –1(x) at the point (–4, 2) is 5.
Because f(x) is an invertible function, the slope of the tangent line to the curve y = f –1(x) at the point (–4, 2) will be the reciprocal of the slope of the tangent line to the curve y = f(x) at the point (2, –4). Since the slope of the tangent line to the curve y = f(x) at the point (2, –4) is –0.2, the reciprocal of –0.2 is 5. Therefore, the slope of the tangent line to the curve y = f –1(x) at the point (–4, 2) is 5.
To determine the slope of the tangent line to the curve y = f^(-1)(x) at a given point, we can use the fact that the inverse of a function has the inverse slope.
Given that the slope of the tangent line to the curve y = f(x) at the point (2, -4) is -0.2, we can consider the following options:
A) The slope of the tangent line to the curve y = f^(-1)(x) at the point (-4, 2) is -0.2.
To determine if this option is correct, we need to find the inverse of the point (2, -4) under the function f(x). If (2, -4) maps to (-4, 2) under f^(-1)(x), then the slope of the tangent line to the curve y = f^(-1)(x) at (-4, 2) is -0.2.
B) The slope of the tangent line to the curve y = f^(-1)(x) at the point (2, -4) is -5.
To determine if this option is correct, we need to find the inverse of the point (2, -4) under the function f(x). If (2, -4) maps to (-4, 2) under f^(-1)(x), then the slope of the tangent line to the curve y = f^(-1)(x) at (2, -4) is -5.
C) The slope of the tangent line to the curve y = f^(-1)(x) at the point (2, -4) is 5.
To determine if this option is correct, we need to find the inverse of the point (2, -4) under the function f(x). If (2, -4) maps to (-4, 2) under f^(-1)(x), then the slope of the tangent line to the curve y = f^(-1)(x) at (2, -4) is 5.
D) The slope of the tangent line to the curve y = f^(-1)(x) at the point (-4, 2) is -5.
To determine if this option is correct, we need to find the inverse of the point (2, -4) under the function f(x). If (2, -4) maps to (-4, 2) under f^(-1)(x), then the slope of the tangent line to the curve y = f^(-1)(x) at (-4, 2) is -5.
E) The slope of the tangent line to the curve y = f^(-1)(x) at the point (-4, 2) is 5.
To determine if this option is correct, we need to find the inverse of the point (2, -4) under the function f(x). If (2, -4) maps to (-4, 2) under f^(-1)(x), then the slope of the tangent line to the curve y = f^(-1)(x) at (-4, 2) is 5.
To find the inverse of a point (x, y) under the function f(x), we swap the x and y coordinates. In this case, the point (2, -4) swaps to (-4, 2).
Therefore, the correct option is:
B) The slope of the tangent line to the curve y = f^(-1)(x) at the point (2, -4) is -5.