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f and g are functions such that f(x) = \frac{12}{\sqrt{x}} and g(x) = 3(2x + 1) (a) Find g(5) (b) Find g(9) (c) Find g^{-1}(6) - Edexcel - GCSE Maths - Question 20 - 2020 - Paper 1

Question 20

$f-and-g-are-functions-such-that--f(x)-=-\frac{12}{\sqrt{x}}-and-g(x)-=-3(2x-+-1)--(a)-Find-g(5)--(b)-Find-g(9)--(c)-Find-g^{-1}(6)-Edexcel-GCSE Maths-Question 20-2020-Paper 1.png$

f and g are functions such that f(x) = \frac{12}{\sqrt{x}} and g(x) = 3(2x + 1) (a) Find g(5) (b) Find g(9) (c) Find g^{-1}(6)

Worked Solution & Example Answer:f and g are functions such that f(x) = \frac{12}{\sqrt{x}} and g(x) = 3(2x + 1) (a) Find g(5) (b) Find g(9) (c) Find g^{-1}(6) - Edexcel - GCSE Maths - Question 20 - 2020 - Paper 1

Step 1

Find g(5)

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Answer

To find g(5), we substitute 5 into the function g(x):

$g(5) = 3(2(5) + 1)$

Calculating this gives:

$g(5) = 3(10 + 1) = 3(11) = 33$

Thus, ( g(5) = 33 ).

Step 2

Find g(9)

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Answer

For g(9), we substitute 9 into the function g(x):

$g(9) = 3(2(9) + 1)$

Now performing the calculation:

$g(9) = 3(18 + 1) = 3(19) = 57$

Therefore, ( g(9) = 57 ).

Step 3

Find g^{-1}(6)

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101 rated

Answer

To find the inverse function g^{-1}(6), we first set g(x) equal to 6:

$3(2x + 1) = 6$

Next, we solve for x:

Divide both sides by 3: $2x + 1 = 2$
Subtract 1 from both sides: $2x = 1$
Divide by 2: $x = \frac{1}{2}$

Thus, ( g^{-1}(6) = \frac{1}{2} ).

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