If f (x) = x^2 + 1 and g (x) = x-4, which value is equivalent to (fxg) (10) ?

Sorry, I always get confused whether I have to do this: f (x) g (x) or this: f (g (x)) but I'll do both and I hope one of them looks very familiar

(f * g) (x) = f (x) * g (x)

(f * g) (10) = f (10) * g (10)

Since you know x = 10, substitute/plug in 10 for x in the equations

f (10) = x² + 1 = (10) ² + 1 = 100 + 1 = 101

g (10) = x - 4 = (10) - 4 = 6

(f * g) (10) = 101 * 6 = 606

(f * g) (x) = f (g (x))

(f * g) (10) = f (g (10)) First find g (10), since we already did you can do this:

g (10) = 6

(f * g) (10) = f (g (10)) = f (6) Now find f (x) when x = 6

f (6) = (6) ² + 1 = 36 + 1 = 37