MHT CET · Maths · Functions
If \(\mathrm{g}(x)=x^2+x-1\) and (gof) \((x)=4 x^2-10 x+5\), then \(\mathrm{f}(2)\) is equal to
- A 1
- B -1
- C 2
- D -2
Answer & Solution
Correct Answer
(D) -2
Step-by-step Solution
Detailed explanation
If \(g(x)=x^2+x-1\) and \((g \circ f)(x)=4 x^2-10 x+5\), then \(f(2)\) ?
1. Relationship:
\(g(f(x))=4 x^2-10 x+5\)
2. Substitute \(g(x)\) : Given \(g(x)=x^2+x-1\), substitute \(f(x)\) :
\((f(x))^2+f(x)-1=4 x^2-10 x+5\)
3. Solve for \(f(x)\) : Use quadratic identities to isolate \(f(x)\). Substitute \(x=2\). After simplifications: Answer: -2, Option 4.
1. Relationship:
\(g(f(x))=4 x^2-10 x+5\)
2. Substitute \(g(x)\) : Given \(g(x)=x^2+x-1\), substitute \(f(x)\) :
\((f(x))^2+f(x)-1=4 x^2-10 x+5\)
3. Solve for \(f(x)\) : Use quadratic identities to isolate \(f(x)\). Substitute \(x=2\). After simplifications: Answer: -2, Option 4.
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