Functions $f$ and $g$ are defined by
• $f(x) = \frac{1}{\sqrt{x}}$, where $x > 0$ - Scottish Highers Maths - Question 12 - 2019
Question 12
Functions $f$ and $g$ are defined by
• $f(x) = \frac{1}{\sqrt{x}}$, where $x > 0$.
• $g(x) = 5 - x$, where $x \in \mathbb{R}$.
(a) Determine an expression for $f(... show full transcript
Worked Solution & Example Answer:Functions $f$ and $g$ are defined by
• $f(x) = \frac{1}{\sqrt{x}}$, where $x > 0$ - Scottish Highers Maths - Question 12 - 2019
Step 1
Determine an expression for $f(g(x))$
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
To find f(g(x)), we first substitute g(x) into the function f. Given
g(x)=5−x,
we substitute this into f:
f(g(x))=f(5−x)=5−x1.
Step 2
State the range of values of $x$ for which $f(g(x))$ is undefined
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
The function f is undefined where its argument inside the square root is non-positive. Hence, we require:
5−x>0
which simplifies to:
x<5.
Therefore, f(g(x)) is undefined for all x≥5.
Join the Scottish Highers students using SimpleStudy...
