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junior college 1 | H2 Maths
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Rachel
Rachel

junior college 1 chevron_right H2 Maths chevron_right Singapore

Hi how do you do part v

Date Posted: 4 years ago
Views: 531
Eric Nicholas K
Eric Nicholas K
4 years ago
gf(x) = g [f(x)]

Values that 'come out' of the function f will 'enter' the function g as inputs.

f(x) = x2 -2x + 2 = (x - 1)^2 + 1

Input of g
= Output of f (the input of f is (1, 3])
= (1, 5]

(curved brackets denote excluding, square brackets denote including)

so output of g
= (1/2 + k/2, 5/6 + k/6]

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Jeremy Sim
Jeremy Sim's answer
12 answers (Tutor Details)
1st
Oh hey, it's the continuation of the question from last week.

Your lecture notes on composite functions should have a page with 3 circles. Those 3 circles are key to understanding composite functions.

To summarise, gf means putting f inside g. We have discovered that range of f was (1,5] last week. So even if g could take values from any value that is 0 or more, there would never be a time where g will take in an input like 7 or 12, since once I go through the function f I will only get values between 1 and 5.

So to find the range of gf, I will need to know what are the set of values g will take due to f and adjust the range accordingly.