Question

Let f(x) = \(\left| {\begin{array}{*{20}{c}} x&1&1\\ {\sin 2\pi x}&{2{x^2}}&1\\ {{x^3}}&{3{x^4}}&1 \end{array}} \right|\). If y = g(x) is image of y = f(x) in y-axis, then absolute value of f(1) g(1) is

Answer 1

Correct Answer - Option 4 : 4

f(–x) = –f(x) = g(x)                                

∴ f(x) . g(x) = – {f(x)}²

or  f(1) . g(1) = –{f(1)}²

= \(-{\left| {\begin{array}{*{20}{c}} 1&1&1\\ 0&2&1\\ 1&3&1 \end{array}} \right|^2}\)

Applying R₃ → R₃ – R₁ ls , then rc

f(1) . g(1) = \(-{\left| {\begin{array}{*{20}{c}} 1&1&1\\ 0&2&1\\ 0&2&0 \end{array}} \right|^2}\) = –(0 – 2)² = – 4