f(x)=f(1-x) for all x

[anguyen]

Q I got wrong in the practice exam - can you pls explain this to me?

For which of the following functions f is f(x)=f(1-x) for all x

a) f(x)=1-x
b) f(x)=1-x^2
c) f(x)=x^2 - (1-x)^2
d) f(x)=x^2 (1-x)^2
e) f(x)=x / (1-x)

The correct ans was D, but I can't get to this...

[sanyalpritish]

This one needs substi. of f(1-x) in the f(x) given in the ans options.
What you need to find out LHS=RHS,
while sub.1-x in all the f(x) given, u will find option D the LHS = RHS

place 1-x into :x^2(1-x)^2=(1-x)^2(x^2)

[jerly_vivek]

Q I got wrong in the practice exam - can you pls explain this to me?

For which of the following functions f is f(x)=f(1-x) for all x

a) f(x)=1-x
b) f(x)=1-x^2
c) f(x)=x^2 - (1-x)^2
d) f(x)=x^2 (1-x)^2
e) f(x)=x / (1-x)

The correct ans was D, but I can't get to this...

for faster calculation, take x=0.
only for D, f(0)=f(1).

[esledge]

for faster calculation, take x=0.
only for D, f(0)=f(1).

I like this method!

People should just be aware of one possible risk (and it's not a big one). Because the question asks which is true "for ALL x," it's possible that more than one answer could "check out" with a particular x value. If that had happened, it's not a big deal. All you'd have to do is pick another value, say x = 2, and check only those remaining answers to see if f(2) = f(-1).