Question

If f(x) = e^x and g(x) = sin x, then the value of (f comp g) (sqrt 2) is ? 2.7 or 3.8

Answer 1

`2.7`

Explanation:

'f comp g' `x = (f @ g)(x)`

this is the same as applying the function `f(x)` to the result of `g(x)`.

here, `g(x) = sin x`, and `f(x) = e^x`

applying `f(x)` to the result of `g(x)` gives `e^(sin x)`.

here, it is assumed that `x` is an angle in radians (rather than degrees).

therefore, when `x = sqrt(2)`, `e^(sin sqrt2) = 2.68522...`

this can be rounded to `2.7`

when `x = sqrt2`, `e^(sin sqrt2) ~~ 2.7`

when `x = sqrt2`, `f(g(x)) ~~ 2.7`

when `x = sqrt2`, `(f @ g)(x) ~~ 2.7`

therefore the value of `(f @ g)(x)` is `2.7` rather than `3.8`.