HELP! I can't solve this probelm?

Question

How many of the following functions have the
property f(x)=f(-x)?
(i) f(x) =x^4 + x^2
(ii) f(x)= cox x
(iii) f(x)=4^x
(iiii) f(x)=17

a) 0
b) 1
c) 2
d) 3
e) 4

Please show me how to do the problem!

edit: (ii) is cos x

Answer 1

d) 3
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Ideas: If f(-x) = f(x), then f(x) is an even function. Among the four functions, only f(x) = 4^x is not an even function.

Answer 2

(i) Remember that x^2 = -x^2. Now x^4 is the same as x^2 squared. So this function qualifies. Try an example

2^4 + 2^2 = 16 + 4 = 20
-2^4 + -2^2 = 16 + 4 = 20

(ii) This one works. Try some examples on a calculator. I imagine the trig functions by picturing a radius of 1 moving around a circle with the centre at the oigin. Cos is the distance from the y axis to the end of the radius. If you start with 0 degrees along the x axis then it doesn't matter whether you go up (+) or down (-) the cos distance is the same and in the same direction.

(iii) Does not qualify. 4^(-x) is the same as 1 divided by 4^x which is obviously not the same as 4^x.

(iv) This function gives the answer 17 regardless of the value of x. So, again, f(x) = f(-x)

Answer 3

2, namely i and iiii

in those 2, substituting -x for x will not change the the function.

(-x)^4+(-x)^2=x^4+x^2

cos x does not = cos -x

4^-x does not = 4^x

f(x)=17, there is no x so any value of x will give you the same f(x) value

Answer 4

d) 3

if x = 1
i) 1^4+1^2 = 2 , (-1)^4+(-1)^2 = 2, yes
ii) cos60 = .5, cos(-60)=.5, yes
iii) 4^1 = 4, 4^-1 = 1/4, no
iiii) f(1) = 17, f(-1) = 17, yes

Answer 5

i)yes
ii)yes
iii)no
iiii)yes