Question

Given f(x)=(1)/(2x-3) on -3,1, find c such that f(c)=0.5 using IVT

Answer 1

To find c such that f(c)=0.5 using IVT for the given function f(x)=(1)/(2x-3) on the interval -3,1, we set the denominator equal to 0.5 and solve for c.

Step-by-step explanation:

The question asks to find c such that f(c) = 0.5 using the Intermediate Value Theorem (IVT). The function f(x) = 1/(2x-3) is continuous on the interval (-3,1). Since f(x) is a rational function, it is defined for all values of x except when the denominator is equal to zero. Therefore, we need to find the value of c that makes the denominator equal to 0.5.

Setting the denominator equal to 0.5 gives us:

2c - 3 = 0.5

2c = 3.5

c = 3.5/2

c = 1.75

So, c = 1.75 is the value that satisfies f(c) = 0.5 using the IVT.