4.1 Calculate the value of $a$ - NSC Mathematics - Question 2 - 2022 - Paper 1
Question 2
4.1 Calculate the value of $a$.
4.2 Calculate the coordinates of the y-intercept of $g$.
Consider: $h(x) = igg(\frac{1}{3}\bigg)^x$
4.3.1 Describe the transla... show full transcript
Worked Solution & Example Answer:4.1 Calculate the value of $a$ - NSC Mathematics - Question 2 - 2022 - Paper 1
Step 1
4.1 Calculate the value of $a$.
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Answer
To find the value of a, we need to isolate a in the equation provided. This might involve using algebraic methods such as substitution or factoring, depending on the context of the problem.
Step 2
4.2 Calculate the coordinates of the y-intercept of $g$.
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Answer
The y-intercept of a function g(x) occurs when x=0. To find this, substitute 0 into the function to determine the coordinates, which will be in the form (0,g(0)).
Step 3
4.3.1 Describe the translation from $g$ to $h$.
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Answer
The translation from g to h can be described in terms of shifts along the x-axis and y-axis. For example, if g is represented as a function that is translated to form h(x), we describe the movement in terms of horizontal shifts and vertical scaling.
Step 4
4.3.2 Determine the equation of the inverse of $h$, in the form $y = ...$
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Answer
To find the inverse of h(x) = igg(\frac{1}{3}\bigg)^x, we first replace h(x) with y: y = igg(\frac{1}{3}\bigg)^x.
Next, we swap x and y: x = igg(\frac{1}{3}\bigg)^y.
Then, take the logarithm of both sides: y=log31(x).
Thus, the equation of the inverse is expressed in this form.
