Question

Let \( f(x) = \dfrac{ax + b}{cx + d} \). Then \( f(x) = x \), provided that:

• A. \(d=-a\)
• B. \(d=a\)
• C. \(a=b=1\)
• D. a=b=c=d=1

Hint:

For identities, equate coefficients of like powers of x.

Answer 1

The Correct Option is B

Step 1: Given (ax+b)/(cx+d)=x
Step 2: Cross-multiplying, ax+b=cx²+dx
Step 3: Comparing coefficients for identity in x, c=0, a=d, b=0
Step 4: Hence required condition is d=a.