Question:
If \( f(x)=\dfrac{4x+7}{7x-4} \), then the value of
\[
f\{f[f(2)]\}
\]
is
If \( f(x)=\dfrac{4x+7}{7x-4} \), then the value of
\[
f\{f[f(2)]\}
\]
is
Show Hint
In composite functions, always evaluate step by step from the innermost function.
Updated On: May 7, 2026
- \( \dfrac{3}{2} \)
- \( \dfrac{2}{3} \)
- \( \dfrac{35}{39} \)
- \( \dfrac{39}{35} \)
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The Correct Option is A
Solution and Explanation
Step 1: Find \(f(2)\).
\[ f(2)=\frac{4(2)+7}{7(2)-4}=\frac{8+7}{14-4}=\frac{15}{10}=\frac{3}{2} \]
Step 2: Find \(f[f(2)] = f\!\left(\dfrac{3}{2}\right)\).
\[ f\!\left(\frac{3}{2}\right) =\frac{4\left(\frac{3}{2}\right)+7}{7\left(\frac{3}{2}\right)-4} =\frac{6+7}{\frac{21}{2}-4} =\frac{13}{\frac{13}{2}}=2 \]
Step 3: Find \(f\{f[f(2)]\ = f(2)\).}
\[ f(2)=\frac{3}{2} \]
Step 4: Final Answer.
\[ f\{f[f(2)]\}=\frac{3}{2} \]
\[ f(2)=\frac{4(2)+7}{7(2)-4}=\frac{8+7}{14-4}=\frac{15}{10}=\frac{3}{2} \]
Step 2: Find \(f[f(2)] = f\!\left(\dfrac{3}{2}\right)\).
\[ f\!\left(\frac{3}{2}\right) =\frac{4\left(\frac{3}{2}\right)+7}{7\left(\frac{3}{2}\right)-4} =\frac{6+7}{\frac{21}{2}-4} =\frac{13}{\frac{13}{2}}=2 \]
Step 3: Find \(f\{f[f(2)]\ = f(2)\).}
\[ f(2)=\frac{3}{2} \]
Step 4: Final Answer.
\[ f\{f[f(2)]\}=\frac{3}{2} \]
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