Let: \( f: A \rightarrow B \) and \( g: B \rightarrow C \) be two functions and \( g \circ f: A ... VIDEO
Let: \( f: A \rightarrow B \) and \( g: B \rightarrow C \) be two functions and \( g \circ f: A \rightarrow C \) is defined. Then which of the following statement(s) is (are) incorrect?
(a) If \( g \circ f \) is onto then \( f \) must be onto
(b) If \( f \) is into and \( g \) is onto then \( g \circ f \) must be onto function.
(c) If \( g \circ f \) is one-one then \( g \) is not necessarily one-one.
(d) If \( f \) is injective and \( g \) is surjective then \( g \circ f \) must be bijective mapping
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions 2023-06-08 Let \( f(x)=a x^{17}+b \sin x \sin 2 x \cdot \sin 3 x+c x^{2} \operatorname{sgn}(\sin x)+d \) \(... 2023-06-08 Consider \( a x^{4}+(7 a-2 b) x^{3}+(12 a-14 b-c) x^{2}-(24 b+7 c) x+1-12 c=0 \), has no real ro... 2023-06-08 \( \begin{array}{ll}\text { Comprehension } & : \theta \text { is said to be well behaved if it ... 2023-06-08 Consider \( a x^{4}+(7 a-2 b) x^{3}+(12 a-14 b-c) x^{2}-(24 b+7 c) x+1-12 c=0 \), has no real ro... 2023-06-08 Let \( f(x)=\ln \left(\frac{3+a \sin x}{b+5 \sin x}\right) \) is odd function then number of pos... 2023-06-08 Let \( A=\{1,3,5,7\} \) and \( B=\{2,4,6,8\} \) and \( f: \mathrm{A} \rightarrow \mathrm{B} \), ... 2023-06-08 Find the domain of \( f(x)=\frac{\sqrt{\cos x-\frac{1}{2}}}{\sqrt{6+35 x-6 x^{2}}} \) 2023-06-08 \( \begin{array}{ll}\text { Comprehension } & : \theta \text { is said to be well behaved if it ... 2023-06-08 The maximum value of the function defined by \( f(x)=\min \) \( \left(e^{x}, 2+e^{2}-x, 8\right)... 2023-06-08 \( \begin{array}{ll}\text { Comprehension } & \text { : If the function } f(x) \text { satisfies... 2023-06-08 Let: \( f: A \rightarrow B \) and \( g: B \rightarrow C \) be two functions and \( g \circ f: A ... 2023-06-08 \( \begin{array}{ll}\text { Comprehension } & : \theta \text { is said to be well behaved if it ... 2023-06-08 \( \begin{array}{ll}\text { Comprehension } & : \text { If the function } f(x) \text { satisfies... 2023-06-08 Comprehension \( \quad: \) Consider a function \( f: R \rightarrow R \) such that \( (f(x)+f(z))... 2023-06-08 Show that \( \left(f \circ f^{-1}\right)(x)=\left(f^{-1} \mathrm{\circ} f\right)(x)=x \) for
(i)... 2023-06-08 Comprehension \( \quad: \) Consider a function \( f: R \rightarrow R \) such that \( (f(x)+f(z))... 2023-06-08 Which of the following statement(s) is/are correct?
(a) Equation \( \operatorname{sgn}(x)=\sin ^... 2023-06-08 \( \begin{array}{ll}\text { Comprehension } & \text { Let the function } f \text { be defined in... 2023-06-08 Let \( f \) be an injective function such that \( f(x) f(y)+2=f(x) \) \( +f(y)+f(x y) \forall x,... 2023-06-08 \( \begin{array}{ll}\text { Comprehension } & \text { Let the function } f \text { be defined in... 2023-06-08 If \( f: R \rightarrow \mathrm{R} \) is an invertible function such that \( f(x) \) and \( f^{-1...