Question

If f(x)= √x and g(x)=2x^3 −x, find f(x)−g(x).

A)2x^3/2+x
B)-2x^3/2-x
C) -2x^3/2+x
D) 2x^3/2 −x

Answer 1

The expression for f(x) - g(x) when f(x) = √x and g(x) = 2x^3 - x is found by directly subtracting g(x) from f(x), which simplifies to -2x^3/2 + x, represented by option C).

Step-by-step explanation:

To find the expression for f(x) − g(x) when f(x) = √x and g(x) = 2x^3 − x, we simply subtract the function g(x) from f(x).

So the calculation would look like this:

f(x) − g(x) = √x − (2x^3 − x)

This simplifies to:

f(x) − g(x) = √x − 2x^3 + x

Since √x can be written as x^(1/2), we can rewrite the expression as:

f(x) − g(x) = x^(1/2) − 2x^3 + x

Therefore, the answer is C) -2x^3/2 + x, which corresponds to our simplified expression with correct signs and exponents.