Question

If y= e(power x) + e(power -x)/2 when y =1

Answer 1

Do you want to know x when y is 1?

y never gets as low as 1, for any value of x.

When x = 0, y = 1.500
When x = -0.4, y = 1.4162
When x = -0.45, y = 1.4286
When x = -0.5, y = 1.4309
When x = -0.6, y = 1.4599

Answer 2

However, knowing how loose folks are with parentheses around here, it's possible she meant

(e^x - e^(-x))/2 = sinh(x)

so,

e^x - e^-x = 2
e^x - 2 - e^-x = 0
clearing the fraction,

e^2x - 2e^x - 1 = 0

this is just a quadratic in e^x

e^x = (2 ± √8)/2
= 1 ± √2

e^x cannot be negative, so we have

e^x = 1 + √2

x = ln(1+√2) = 0.88137

check: asinh(1) = 0.88137