Hi,
If you calculate the gain bandwidth product required for your app you can tell right away that an amplifier might not work in this app, at least in a single stage.
I see the data sheet for the TL082 as spec'ing a GBW (gain bandwidth) of 3MHz, not 4MHz. That means with a gain of 1 we might be able to pass a sine signal at 3MHz assuming the output amplitude is not too high (less than 0.7 volts peak). But a gain of 1 doesnt help at all here, and an output of 0.7 volts certainly doesnt help either.
Also, with a gain of 7 and an output of 14v peak the TL082 bandwidth would be limited to about 150kHz, so yes it will attenuate after that.
So what does it take...
To get a gain of 7 at 3MHz and produce a sine signal a the output that goes up to 14v peak we would need an op amp that has a minimum gain bandwidth of 21MHz, and a slew rate minimum of 264 volts per microsecond. That's to do it all in one op amp section.
But that is just the op amp specification to handle a sine wave. Luckily, the triangle wave has a rate of rise with time less than the max for the sine wave, so we'd be covered for the triangle wave too.
However, now we come to the square wave. An ideal square wave has to have a rise time that is infinite, and that is impossible to reproduce. Going slightly non ideal, we can use a rise and fall time that is just much faster than the pulse width. If we agree that a rise and fall time of one-tenth of the pulse width is good enough at the max frequency of operation, then the rise time has to be 33ns. To rise to 14 volts in 33ns we would need an op amp that has a slew rate of at least 420 volts per microsecond.
However, that's not the best way to do it. The best way would be to use a different circuit for the square wave and use a transistor output stage like maybe a MOSFET. The op amp would handle the sine and triangle, and the transistor(s) would handle the square wave output.