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Question

lf f(x)=lx and a,b,c are in A.P. k,l are constants. Then f(a−k),f(b−k), and f(c−k) are in

A
A.P
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B
G.P
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C
H.P
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D
A.G.P
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Solution

The correct option is A A.P
f(x)=lx
f(ak)=l(ak) a=K+f(ak)l
f(bk)=l(bk) b=k+f(bk)l
f(ck)=l(ck) c=k+f(ck)l
a,b,c are in A.P
2b=a+c
2(k+f(bk)l)=k+f(ak)l+k+f(ck)l
2f(bk)=f(ak)+f(ck)
So, f(ak),f(bk),f(ck) are also in A.P.

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