Question

If f(x) = cos x + sin x and g(x) = x2 – 1, then g(f () is injective in the interval
A
[0, 1]
B ]
(-4,1)
C]
D (0,7)​

Answer 1

Answer:

MATHS

If f(x)=sinx+cosx, g(x)=x

2

−1 then g(f(x)) is invertible in the domain.

ANSWER

f(x)=sinx+cosx,g(x)=x

2

−1

Theng[f(x)]

g[f(x)]=g(sinx+cosx)=(sinx+cosx)

2

−1

g[f(x)]=sin

2

x+cos

2

x+2sinx.cosx−1

=1+2sinx.cosx−1[∵sin

2

x+cos

2

=1]

g(f(x))=sin2x

Ans.[∵2sinx.cosx=sin2x]

Letg(f(x))=y

y=sin2x[∵Domainofsinxis

2

−π

,

2

π

]

∴Domainofsin2x=[

2

−π

,

2

π

]Ans.

Step-by-step explanation:

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