f(x)=x^2 + 2x g(x)= radical sign(2x-1)

Question

Find f⋅g and f + g (This combining functions)

Answer 1

Here you go:

Let f(x) = x² + 2x and let g(x) = √(2x-1).

By definition of function composition:

f compose g, otherwise known as f°g is defined as follows: f°g = f(g(x)).

Similarly, g°f = g(f(x)).

When we write out f(g(x)), for every x within the equation f(x) = x² + 2x, we substitute √(2x-1) in for every x, as follows:

Noting that f(x) = x² + 2x and g(x) = √(2x-1)

f°g = f(g(x)) = (√(2x-1))² + 2(√(2x-1))

Also: g°f = g(f(x)) = √(2(x² + 2x) -1)

For Part 2, when we write out f+g, this is written as f(x) + g(x) and done by simply adding the two functions, as follows:

f + g = f(x) + g(x) = (x² + 2x) + √(2x-1) .

Hope this helps. Feel free to comment with any questions you may have regarding this problem. Happy to help. And if you like my solution please feel free to leave a positive review. Thanks.