The graphs of `y=f(x)` and `y=g(x)` are shown.
Which graph best represents `y=g(f(x))`
Functions, 2ADV F1 EQ-Bank 11
Given the function `f(x) = sqrt(3 - x)` and `g(x) = x^2 - 2`, sketch `y = g(f(x))` over its natural domain. (2 marks)
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`g(x) = x^2 – 2,\ \ f(x) = sqrt(3 – x)`
| `g(f(x))` | `= (sqrt(3 – x))^2 – 2` |
| `= 3 – x – 2` | |
| `= 1 – x` |
`text(S)text(ince)\ \ f(x) = sqrt(3 – x),`
`=> text(Domain:)\ x <= 3`