Photo AI

Let $f(x) = 3x + 5$, for $x \in \mathbb{R}$ - Junior Cycle Mathematics - Question 4 - 2015

Question icon

Question 4

Let-$f(x)-=-3x-+-5$,-for-$x-\in-\mathbb{R}$-Junior Cycle Mathematics-Question 4-2015.png

Let $f(x) = 3x + 5$, for $x \in \mathbb{R}$. (a) Find the value of $f(7)$. (b) Write $f(k)$ in terms of $k$. (c) Using your answer to part (b), or otherwise, find... show full transcript

Worked Solution & Example Answer:Let $f(x) = 3x + 5$, for $x \in \mathbb{R}$ - Junior Cycle Mathematics - Question 4 - 2015

Step 1

Find the value of $f(7)$.

96%

114 rated

Answer

To find the value of f(7)f(7), substitute xx with 7 in the function.

f(7)=3(7)+5=21+5=26.\begin{align*} f(7) & = 3(7) + 5 \\ & = 21 + 5 \\ & = 26. \end{align*}

Thus, f(7)=26f(7) = 26.

Step 2

Write $f(k)$ in terms of $k$.

99%

104 rated

Answer

We can express f(k)f(k) by substituting xx with kk in the function:

f(k)=3k+5.\begin{align*} f(k) & = 3k + 5. \end{align*}

Step 3

Using your answer to part (b), find the value of $k$ for which $f(k) = k$.

96%

101 rated

Answer

To find the value of kk for which f(k)=kf(k) = k, we set the equation:

3k+5=k.3k + 5 = k.

Rearranging gives:

3kk=52k=5k=52.\begin{align*} 3k - k & = -5 \\ 2k & = -5 \\ k & = -\frac{5}{2}. \end{align*}

Thus, k=52k = -\frac{5}{2}.

Join the Junior Cycle students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;