Question

Can someone explain to me the steps how they got 2 √4^2+2x-3-2 from this question…

Given the following equations, determine the simplified expression:
f(x) = 2x^2 + x - 1 g(x)= √2x-1 h(x) = -2
Determine the simplified expression of 2g(f(x))+h(x)

Answer 1

Explanation:

with your square root symbol I never know what is inside the square root and what is possibly outside.

so, I can only guess and see what comes close.

f(x) = 2x² + x - 1

g(x) = sqrt(2x - 1) ??? is that so ?

h(x) = -2

2g(f(x)) + h(x)

g(f(x)) means that the whole f(x) expression is used as x in g(x).

the whole combined function is then

2×sqrt(2(2x² + x - 1) - 1) - 2

2×sqrt(4x² + 2x - 2 - 1) - 2

2×sqrt(4x² + 2x - 3) - 2

and if I am not mistaken, then this is the solution you mentioned at the beginning (if I try to read between the typos and missing info).

this is how people get to this.

do you understand it now ? or is there still something unclear ?