Find the roots of the function f(x) = (2^x − 1) - (x2 + 2x − 3) with x ∈ R.

There are no real roots.

Step-by-step explanation:

To find the roots of the function

f(x) = (2^x − 1) - (x2 + 2x − 3) with x ∈ R.

First open the bracket

2^x - 1 - x^2 - 2x + 3 = 0

Rearrange and collect the like terms

2x^2 - x^2 - 2x + 3 - 1= 0

X^2 - 2x + 2 = 0

Factorizing the above equation will be impossible, we can therefore find the root by using completing the square method or the quadratic formula.

X^2 - 2x = - 2

Half of coefficient of x is 1

X^2 - 2x + 1^2 = -2 + 1^2

( x - 1 )^2 = - 1

( x - 1 ) = +/- sqrt(-1)

X = -1 + sqrt (-1) or -1 - sqrt (-1)

The root of the function is therefore

X = -1 + sqrt (-1) or -1 - sqrt (-1)

Since b^2 - 4ac of the function is less than zero, we can therefore conclude that there is no real roots

step-by-step explanation: