Question

If f (x) =2x^3 + 2x -3 and g(x) = -0.5 |x-4|. What is the value for f(x) = g (x) ?

A. X = 0
B. X = -1.75
C. X = 4
D. X = 0.5

Answer 1

D. x = 0.5

Explanation:

A graphing calculator is the quickest way to get to an answer here.

f(x) = g(x) for x = 0.5

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We can find the y-intercepts of the two functions to be ...

f(0) = -3

g(0) = -2

We know the x-intercept of g(x) is x=4. The x-intercept of f(x) will be a value less than 1, because f(1) = 1. (The function crosses the x-axis between x=0 where f(x) < 0 and x=1, where f(x) > 0.)

Considering these intercept points, we know the value of x for f(x)=g(x) will be between x=0 and x=1. There is only one answer choice in that interval:

x = 0.5